Quite unlikely. Some biomedical engineers work on actual clinical problems. For example, engineers working at the hospitals. And people who do surgeries/operations are likely to work on human bodies and they may see blood. But usually people carrying out operations tend to be a team of qualified medical doctors and nursing staff. Engineers are less likely to get involved in an actual operation. Their work would usually be with various machines used for sugeries etc.
As a graduate engineer, I use to work at the hospitals. I use to work on X-ray machines used for fixing clogged hearts. But most of my work with X-ray machines was before surgery, like ‘making sure everything is working properly’ and after surgery, like ‘doing calculations on the X-ray images of the heart’. I hardly came across any blood in my job.
Also, biomedical engineering is a huge area. Some biomedical engineers may not come in contact with any human body at all. For example, a biomedical engineer could be working on how to transfer patient’s heart rhythm to a doctor. Patient may be at home or in an ambulance. And doctor might be sitting in an hospital. This is called as ‘Biotelemetry’. But the biomedical engineer doing this work may never see the patient.